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orthonormal comments on Cascio in The Atlantic, more on cognitive enhancement as existential risk mitigation - Less Wrong
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No, you said, as I quoted, that intelligence was not at all correlated with atheism, despite atheism being highly correlated with intelligence. This is uncontroversially and trivially impossible; if p(A|B)≠p(A) where p(A) and p(B) are positive, then p(B|A)≠p(B).
The coefficient of correlation between A and B is the same as the coefficient of correlation between B and A, so this is false. I believe you mean, rather, that having a positive test for a rare disease can still leave you less than 50% likely to have the disease, while having the disease makes you very likely to test positive for it. However, the correlation is still strong in both directions: your chance of having the disease has jumped from "ridiculously unlikely" to just "unlikely" given that positive test.